I guess I should elaborate a bit more on the Wallace-Simpson Line, considering it is used to make a picture that produces the same reaction every time I show it to my kids: THAT is frickin' COOL!
The envelope of every Wallace-Simpson line for every point on the circumcircle is the Steiner deltoid whose area is half the area of the circumcircle. The Steiner deltoid is also tangent to the Nine-Point Circle, the unique circle that passes through the midpoints of the sides of the triangle.
Click on the small animation button in the lower left corner. Click on the reset icon in the upper right corner erase the traces.
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